A New Cluster Validity Index and its Application in Image Segmentation

Estimating the optimal number of clusters in an unsupervised partitioning of data sets has been a challenging area in recent years. Although many cluster validity indices for this estimation have been developed, there is not an accurate way to find the best number of partitions. Most of the indices consider compactness and overlap or separation measures, to estimate the quality of partitioning. As it will be mentioned, some of previous separation measures does not measure the separation of clusters in a proper way and give the same grade of separation for clusters that are differently overlapped. In order to overcome this shortcoming, in this study we introduce a new separation measure, which measures the separation of clusters considering the degree of fuzziness of data in the intersection of them in addition to the distance between the centers of clusters. The new index which uses this separation measure is tested on various artificial and standard data sets. Also it is tested on 2 image data sets. The results show that the proposed index can efficiently find the number of clusters in the datasets relative to the previous indices. Also it is robust dealing with noisy and large datasets.